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Gabriel Scarmana
School of Civil
Engineering &
Surveying
An application of the least squares plane fitting
interpolation process to image reconstruction
and enhancement
Presented at th
e FIG W
orking Week 2016,
May 2-6, 2
016 in Christchurch, N
ew Zealand
A set of low-resolution shifted images are combined at sub-pixel
level via multi-frame image enhancement to obtain an improved
image.
Purpose: Improve Image Quality
Low-resolution imagery High-resolution imagery
The process usually involves an image enhancement technique
referred to as image Super-Resolution (SR).
Multi-Frame Image Enhancement: What Is It?
Math
Calculates fractional image shifts Produces a finer resolution composite
The Principle
An idealised super-resolution setup. Images (b)-(d) are taken with a
sub-pixel shifts of half a pixel in the horizontal, vertical and diagonal
directions in relation to image (a). Their pixels can then be
interleaved to generate a double resolution image.
(a) (b)
(c) (d) (SR)
Sub-pixel shifts cause images to be different
In a real world, the randomness of the motions (or sub-pixel shifts)
between low-resolution images of the same object cause these
images to be different as they are sampled at different positions.
a
dc
b
Image Registration/MatchingImages can be represented as surfaces of pixels intensities. Area
based registration techniques can determine the position of each
image from the first with an accuracy of 0.1 units (i.e., 0.1 pixel).
The unknown value of the high-resolution pixels (white cell in the
centre of the grid) will be estimated based on values of the
surrounding pixels of the low-resolution images.
Merging the Low-Resolution Pixels
n points are selected near the
new sample position. A least
square plane is fit through
those n points and the value of
this plane at the new position is
the new pixel value. This
method (a) is fast (b) it uses the
information of data position (c)
it estimates the accuracy of
each high-resolution pixel and
(d) does not create blurring
artifacts.
Least Squares Planes Fitting
What Accuracy Can Be Achieved?
+/- 5
High-resolution composite
High-resolution composite Original
50 low-resolution compressed images
Magnification = 4
How Many Images Are Required?
The number of low-resolution images generally depends on
the magnification factor required, the distribution of the sub-
pixel shifts and the amount of noise present in the imagery.
Magnification (p)
No
. o
f im
ag
es
No. of images = 4p2
Limitations
Rotations, distortions and scale differences may decrease the
quality of the enhancement because the images must be
brought into alignment first using warping/morphing techniques.
Colour Images
Colour images are first split
into their RGB (Red, Green
and Blue components). Each
component is enhanced
separately and the results
are then merged.
Low-resolution colour images
Traffic Surveillance
The car of interest in the red box and its
trajectory. (a) an enlarged low-resolution view
of the vehicle as per original video footage
and (b) the enhanced image of the car.
a
b
Forensics
A composite was made from a set
of in-taxi images; this led to an
admission by the suspect of being
in the taxi, but the suspect was
acquitted of the robbery charge.
Higher resolution composite
Conclusions
Multi-Frame image enhancement processes are a highly
effective way to improve the quality/ resolution of video and
still images.
In principle, the quality of the images as enhanced by the
proposed method depends on the amount of noise present
in the low-resolution images, (b) the number of low-
resolution input images and (c) the magnification factor
required to meet resolution requirements and (d)
atmospheric distortions.
Gabriel Scarmana
School of Civil
Engineering &
Surveying
An application of the least squares plane fitting
interpolation process to image reconstruction and
enhancement
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